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Raman shifts of the soft mode A$_{1g}$ and the B$_{1}$ mode are calculated at various pressures at room temperature for the cubic-tetragonal transition (P$_{C}$ = 9.5 GPa) in SrTiO$_{3}$. This calculation is performed using the observed volume data through the mode Gruneisen parameters of A$_{1g}$ and B$_{1}$, which vary with pressure, by fitting to the experimental wavenumbers in this crystalline system. Calculated Raman shifts are then used as order parameters to predict the pressure dependence of the damping constant and the inverse relaxation time for the cubic-tetragonal transition in SrTiO$_{3}$. Our predictions from the pseudospin-phonon coupling and the energy fluctuation models can be compared with the experimental measurements when available in the literature.

Calculation of the frequency shifts and damping constant for the Raman modes (A$_{1g}$, B$_{1})$ near the tetragonal-cubic transition in SrTiO$_{3}$